Bases invariantes de friabilit\'e

TL;DR

This paper constructs models of finite fields with invariant smoothness bases under automorphisms to improve the efficiency of discrete logarithm algorithms.

Contribution

It introduces methods to build finite field models with automorphism-invariant bases, aiding in faster discrete logarithm computations.

Findings

Models for finite fields with invariant bases are constructed.

Such bases can accelerate discrete logarithm algorithms.

The approach enhances computational efficiency in finite field cryptography.

Abstract

Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for computing discrete logarithms in some finite residue fields.